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Alge-Tiles an Overview

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x Set 1 1 x2 Set 2 xy y2 y

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x – x = 0 –1 1 x2 – x2 xy y2 –y2 – xy y – y

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Adding Integers (+ 5) (+ 7) + = 12

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Adding Integers (– 5) + (– 7) + = – 12

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Adding Integers (– 5) = + 3

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Subtracting Integers (– 2) – (– 4) – + = 2

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Subtracting Integers (– 4) – (+ 6) – + = – 10

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Multiplying Integers 6 (2)(3) –6 (2)(–3) (–2)(–3) 6

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**Algebraic Expressions**

x2 + 2x + 4 x2 – 3x – 2 2x2 – x + 2

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Adding Polynomials (4x + 5) + (2x – 3) + = 6x + 2

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**Subtracting Polynomials**

(5x + 2) – (3x – 4) – + = 2x + 6

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**Multiplying Polynomials**

3(x + 2) x + 2 3 Guiding tiles

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**Multiplying Polynomials**

3(x + 2) 3x + 6

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**Multiplying Polynomials**

x(x – 3) x – 3 x Guiding tiles

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**Multiplying Polynomials**

x(x – 3) x2 – 3x

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**Multiplying Polynomials**

(x + 2)(x + 3) x + 2 x + 3 Guiding tiles

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**Multiplying Polynomials**

(x + 2)(x + 3) x2 + 5x + 6

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**Multiplying Polynomials**

(x – 2)(x + 2) x – 2 x + 2

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**Multiplying Polynomials**

(x – 2)(x + 2)

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**Multiplying Polynomials**

(x – 2)(x + 2) x2 – 4

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**Factoring Polynomials**

x2 + 6x + 8 x + 4 x + 2 Form a rectangle x2 + 6x + 8 = (x + 2)(x + 4)

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**Solving Equations: solve for x**

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**Solving Equations: solve for x**

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**Solving Equations: solve for x**

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**Solving Equations: solve for x**

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**Solving Equations: solve for x**

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**Solving Equations: solve for x**

3x – 1 = x – 5

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**Solving Equations: solve for x**

3x – 1 = x – 5

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**Solving Equations: solve for x**

3x – 1 = x – 5 x = –2

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**Both sides have seven white tiles.**

Check Substitute for 3x – 1 = x – 5 x = –2 Both sides have seven white tiles.

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